Microscopic Origin of Spin Splitting in Altermagnetic CrSb Thin Films

Abstract

Altermagnets have recently emerged as promising materials for spintronic applications owing to their momentum-dependent spin splitting. Among them, metallic CrSb is particularly attractive owing to its giant spin splitting and high N\'eel temperature. However, the microscopic origin of the distinct spin-splitting behaviors in bulk and thin-film CrSb remains unresolved. Here, we systematically investigate the electronic structures of CrSb slabs with different surface orientations using first-principles calculations. Although all considered slabs preserve spin-group symmetries compatible with altermagnetism, they exhibit markedly different electronic structures: the (2$\bar{1}\bar{1}$0) slab retains pronounced altermagnetic spin splitting, whereas the (0001) and (10$\bar{1}$0) slabs display nearly spin-degenerate bands. We demonstrate that dimensional reduction fundamentally changes the microscopic origin of altermagnetic spin splitting. Unlike bulk CrSb, altermagnetic spin splitting in thin films requires long-range inter-unit-cell coplanar Cr--Sb hopping, while Sb--Sb hopping provides an additional contribution. The preservation or suppression of these hopping pathways explains the strong surface dependence of the spin splitting. Our findings establish a microscopic mechanism for understanding altermagnetism in reduced dimensions and provide a general principle for engineering spin splitting in low-dimensional altermagnetic materials.